Hi Bonaqua123,
Hmm, certainly a dilemma. Not sure if you have already made up your mind, but for anyone else in the same predicament let me explain how hiring works in the BA world.
For background, I should explain that I am a BA Manager with over 25 years experience as a BA, and a number of those as a BA Manager. I hire (and occasionally fire) people fairly often. I am based in the UK, but it much the same for the US.
So, to your question. When you look to hire a BA there is a list of things, in a particular order, that you look for in a CV:
1. Can he/she do the job? - e.g. experience and skills
2. Do they seem keen?
3. When are they available?
4. Is there anything to suggest that something isn't right?
The first point is often the one that either gets you into the "Seems good" pile of CVs or the straight into the rubbish bin. You have some experience of being BA which is good. Typically I would look for at least two years experience. It doesn't have to be in a like for like role, just the fact that you have the basics is enough and this point. On this, you clearly qualify.
The second point is how you interpret their CV. I assume you applied for this role, and the hirer will have seen that it is different from what you did previously, so I would say it shows that you are at least reasonably keen. By the way, what I mean by 'keen' is that if I offer the role to you, you aren't going to turn around and say to me 'Na, not really what I am looking for". This is the most annoying thing for hirers as each new role can cost up to £5,000 per application (If the role is offered). Bare in mind that they need to carry out the relevant checks, spend time looking through CVS etc. This is a hard one to judge for the hirer and mistakes do happen.
The third point should have been made obvious in your CV or via the agency if you went through one.
The fourth point is interesting. This should act as a warning to all BAs applying for a new role. The first thing I look out for is consistency - do all of your dates on your CV make sense? Is there a role which you were there for under a year, if so why?
So, to answer your personal points. Clearly they think you have what it takes by offering you the job. That's a good start. However, as you say, you are unsure whether the role is a good fit. So, this is a key point and this goes out to all BAs.
Be careful not to button hole yourself to a particular type of BA role - in your case Digital BA. There are only so many jobs out there for particular BA roles, even ones that are currently in fancy. What happens when Digital BA roles are either non-existent (as you are finding now) or if there is a change to how companies employ people. For example, do they look more to Developers to do this for Digital projects? Its happened before, so you need to protect yourself from that.
Experience in another sector, or a different type of role can work both ways. It allows you to apply for more varied jobs, you get a greater understanding of more techniques, systems etc. BUT it can also work against you. It shouldn't but it can. Some (Not me by the way) hirers may look at your CV and say, well why did you do that role then? This you mention, but I think you are fairly safe from this because your experience as a BA is relatively small. So there isn't a theme set yet in your career.
You say that you want to stay in Digital projects, but how do you know what you prefer if you haven't tried others. Also, working for a legacy technology company is not a bas thing - it would show me that you are flexible and can promote new ideas. The biggest challenge to any project worker is getting people to accept change. Often, especially older companies, they wont be happy about this, but that is part of the challenge for these types of role.
So what should you do? You say that you have tried to get a new role for a few months. Major point here - any gap in your employment longer that 3 months and you fall into "Is this something I should be worried about" category. I would start to ask why you haven't worked for so long. Especially so, since you took time off. People will assume (wrongly probably) that you aren't good enough, your trouble, and you just aren't very good. Its harsh, but there are lots of BAs out there wanting a job, so why risk it with someone who has unknown issues?
Personally, I would take the role, carry on looking for your Digital BA job that you want, and if offered one that you think meets everything you want in your next role then take it up. You can always leave if needs be. If the interviewer asks why you are applying so soon, be honest, say that you took the contract role to gain more experience until such time as you got a role you dreamed of (ham it up a bit here) such as this one (the Digital role).
If you cant find a Digital role, then at least you have something on your CV to fill the gaps, you have more experience and some money in your bank account.
One last thing, which you mention about is changing from a contract role to a permanent role. As a rule of thumb, contract roles are paid much better, but you don't get the perks and obviously you aren't there indefinitely. Moving from one to the other can difficult but it really shouldn't be. If you move from Perm to contract its probably easier. But moving the other way Interviewers will often ask you "why?" My tip again, is be honest. What Hirers are worried about in this situation is that you wont appreciate the difference in money, be at the perm company for 4 months, then notice the hit to your wallet and leave. So in your interview you have to make it really obvious to the Interviewer that you are looking for stability. Forget money, you want to see the Change you put in place grow and actually see the end results (most contractors will already have left before they get a chance to see the fruits of their labours).
I shouldn't really say this as a Hiring Manager, but you can always leave a role, but you cant just walk into one when it suits you. So take the role, carry on looking and applying for the Digital roles, and if you are lucky enough to be offered a Digital role, take it up.