I've got a Thumb BO 5 and it is an instrument I'd never be without. However, they are very different to a Squier P, but when you know you want a Thumb, nothing else will do - not even another Warwick.
I was actually talking to my brother about the Thumb as a design earlier this evening and it really is a unique bass, it's quite different even to other basses in the Warwick line. The body is small (especially on the BOs), very heavy and the way the weight is distributed gives some people issues with neck dive. THe way it sits on the body means the 1st fret is quite a long way away, compared to where it would be a on a P bass. If you wear a Thumb on a strap, it hangs over to the left of your body, if you wear a Fender P or J it hangs over to the right. I use a Warwick strap, it's pretty wide and grippy and I don't have issues with neck dive. My Thumb is an ovangkol body and neck and it does weigh a lot. Those dense, heavy woods are part of what makes the sound - the way a Thumb resonates when you play it is like no other bass, Streamers, Corvettes etc just don't feel the same.
The pickup postioning on the 5 is a key to the classic Thumb sound too imo, the two single coils slanted and stacked as close to the bridge as possible really helps to emphasise the punch and growl the Thumb is known for. When it comes to growl, all Warwicks growl to a degree but the Thumb is the one that really has the guts and growl more than others, however it's not exactly a versatile sound and you can tame the aggression but never really remove it.
Try to avoid the broadnecks if you can't play one first. They really are huge, brutal things to play. None of the necks are tiny on the Thumbs, But the BNs are massive.
I'd probably aim to buy a used one, there seem to be plenty in circulation and some bargains can be had on second hand basses.
The jump from a Squier to a real German-made Warwick might seem like a big jump, but truth be told, when you want a Thumb there is no substitute. No Streamer or Corvette will do the job.