Solihull is more pretentious than Sutton Coldfield (although the nearer to Four Oaks you are - especially in it - it gets pretty pretentious too). Solihull seems to make a big deal - and pride itself - on not being part of Birmingham, which can be really annoying as a Brummie (because it's generally said in a derogatory way).
Almost all the schools in Sutton Coldfield are either Good or Outstanding - most of the ones that were either a 3 or a 4 have been academised, so are awaiting Ofsted inspections - but be aware most of those Good and Outstanding inspections were at least 5 years ago.
Sutton also has the grammar schools for secondary, if that's important to you - from Solihull it would be a bus into Birmingham for King Edwards.
Solihull has some great schools, but as mentioned, be aware that Solihull authority covers a wide ranging area, with a variety of socioeconomic backgrounds - Chelmsley Wood, Smiths Wood and Kingshurst are all Solihull areas, but don't always have the best reputations (personally, I regularly shopped in Chelmsley Wood and went to secondary school in Kingshurst, but it wouldn't be for everyone I don't think).
Sutton Coldfield has the Gracechurch shopping centre, but last time I was there (admittedly a few years ago) it was looking tired and I think they were going to do some regeneration work to it.
Both are easy to get into Birmingham City Centre from if you want/need to, but traffic from (and then to) can be bad at rush hour, as previously mentioned.
I would pick Sutton Coldfield just because it has the park, which although it can get busy, is a lovely space!