I had a Petrel 2 and an H3. After having them both for a bit, I sold the Petrel 2. I like the H3 better.
For me, the H3 size is way better than the Petrel or Perdix. The H3 buttons are easier to operate, especially with gloves on. The display is just as easy to read.
That said, I would like to get a 2nd tech computer to use as a backup on tech dives. Right now, I have an Oceanic Atom 3.0 for recreational diving and I use it as my backup on tech dives. So, I have been looking around, trying to decide what to get. I have determined that I would not buy another tech computer right now unless I had to (i.e. my H3 died). I like the AI on my Atom. I want the option to use AI on whatever tech computer I buy. The ScubaPro version of the H3 is supposed to be released around the beginning of November and have an AI option. So, I am waiting to see what happens there.
If my H3 died and I DID have to get a new tech computer right now, I would work out something with a friend in England or Canada and order a Heinrichs Weikamp OSTC3, to be delivered to my friend who would then ship it over to me. The OSTC3 looks nicer than the Perdix, to me, and is only about USD$700. For you (the OP), if you're not worried about having Trimix capability, the HW OSTC Sport would do everything you would need and it's even cheaper. It is virtually identical to the OSTC3 except for not supporting Trimix and not having a fiber optic cable connector on the outside.
All that said, if I were buying a computer and I had no plans for tech training to start deco diving, then I wouldn't bother with any of those tech computers. An Oceanic computer running the DSAT algorithm will allow you more bottom time. When I had the Petrel 2, I only used it on recreational dives as a backup to my Atom, in case the Atom died (which I've never had a lick of trouble from). Now, for Rec dives, I use the H3 as backup to the Atom. The Atom runs the DSAT algorithm and it consistently allows me longer NDLs than a tech computer does, unless you set the Gradient Factors really high (which you cannot do with a Shearwater in OC Rec mode). And if you haven't gotten training on deco theory and Gradient Factors, then maybe you shouldn't even be messing with those as custom settings anyway.
TL;DR: I don't think the Perdix is the best tech computer on the market, and I'm not sure how many people who say it is have really looked at the OSTC3 or OSTC4 (even better, but too expensive for me!). I don't think the Perdix is BETTER than the H3, either. But, if I weren't getting tech training and doing deco dives, I would stick with a recreational computer.
Just because a F1 car is the best thing for a racetrack doesn't mean it's the best car for commuting to work and weekend road trips.
If you do get a Rec computer and you do eventually exceed the NDL, you can simply do the stops it tells you to on your ascent and it won't lock you out. And a Rec computer running DSAT is liberal enough that if you do exceed the NDL, I would DEFINITELY do all the deco stops it tells you and not skip even one minute. Skipping the deco prescribed by one of those is NOT like skipping 1 minute of deco that is prescribed by a tech computer with GF 30/70...
Just my $0.02...
ps. You said you want to upgrade your setup. What do you have and what is it that you don't like and want to improve on?