To get to the nitty gritty of the costs, take a look at
http://www.thesalarycalculator.co.uk/salary.php and take a look at your take home pay (taxes are higher here and you will still have to file in the US. You shouldn't owe unless you have investments or other assets that are subject to taxation).
Based on £35k, your take home pay will be £2,200 a month. This could decrease if you have a company car, private medical coverage (NHS will cover you and you will not *need* private coverage), pension, etc.
Looking at Portsmouth on Rightmove.co.uk, shows that you would have a lot of options for a 2 bed flat for £700/month.
Other expenses (all estimates) if anything, I've gone a bit high:
Council tax: £100/month
TV License: £150/year
Gas / Electric: £85/month
Water: £30/month
Cable/Broadband/Phone: £55/month
Mobile Phone: £35/month (£70/month for two people)
Car Insurance: £50/month (won't need if you don't have a car of course)
I may be forgetting something, but I think this basically covers most things. That basically takes your bills to £1,100 a month, leaving £1,100 left over to cover food/entertainment/travel or £250 a week.
One off expenses in your first year will be driving lessons to get a UK driving license (you can drive on your US license for a year). It will probably cost £400ish to get your license with5 hours of lessons and the test fees.
If you don't have a furnished apartment, you'll need furniture and such. If you have pets, they are expensive to move.
Eating out is more expensive here, costing about £40 to £50 for a meal out for two (obviously can go to cheaper places or more expensive places). Train travel is very expensive (I talk to people in the US who have the misconception that train travel is cheap. It's not cheap, but it is a very good network).
Obviously cost is not everything. You will be opening yourself up to having international experience on your resume which will open many other opportunities. Granted, if you don't want to get yourself into an international "niche", this is something to consider too.
Also if you were to love it, the requirements to obtain ILR (permanent residence) are becoming harder all the time. If you will be a Tier 2 General, you will need to make GREATER than £35k for five years to qualify. If you will be on a Tier 2 ICT, you will not be able to qualify for ILR. Something to keep in mind if you were to fall in love in the UK and want to make this your permanent home.
Good luck to you. You are in an awesome position to have two great choices!