HDR is the bigger reason to upgrade over the resolution boost in my opinion. Gaming has a lot more fine lines than film though so it will make a difference having a 4k screen but depending on the size of the TV and distance you sit will make a big difference to how much of an upgrade the increased resolution makes.
Obviously budget makes a difference in the quality of the HDR and how much of the High Dynamic Range you actually get. Games can be up to 10000nits in brightness which obviously has a very high range and no TV can actually deliver that - yet. Therefore the content has to be limited to the TV's capability. Budget TV's too tend to be LED's with edge lit technology which can lead to blooming - a very bright Logo on a solid black background will be very difficult to do without the backlight affecting the black quality. The majority of games are full screen so you don't have to worry about uneven black bars though.
As others have said, HDR isn't about 'brightness' but about the range. A TV that only hits 500nits, even with perfect blacks, isn't able to deliver the range that a TV at 1000nits can. It has to limit the content down to its capability and/or clip the highlight details. Colour range too matters and the wider the colour Gamut and greater the contrast range, the better the HDR presentation and closer it will get to the Master. Colour volume matters with HDR and the 'best' have the greatest colour volume. If a Neon Red (or a Lightsabre) is meant to be displayed at 1000nits for example, some TV's won't be able to display that as 'red' as it should be or as bright either because they don't have the colour gamut or as high a dynamic range necessary to display that. There are quite a few games with HDR Neon and Lightsabres in HDR so the quality of that does vary considerably between TV's. If you are only used to SDR, its still an upgrade and can still look 'impressive' but it can still be a long way from being displayed as intended or as good as it could be. IF you are used to gaming on a 540p, 720p looks like a great upgrade, but its still not as good as 1080p offers...
Another consideration is the future. We are expecting next gen in a year (or less) and they will take advantage of HDMI 2.1 with Variable Refresh Rates (VRR), High Frame Rate (HFR - 4k at up to 120fps), eARC etc. Currently, only LG's OLED TV's (I believe) offer HDMI 2.1. Samsung Q series offer VRR. None of these are needed for the PS4 Pro though but maybe a consideration IF you are likely to upgrade your console in a year or so. If you don't want to upgrade your TV again for quite a while, then maybe consider which TV has the most 'future proof' features. I know the Future can change and nothing is totally future proof but there is no doubt HDMI 2.1 is going to be used for next gen gaming consoles.
At the end of the day, its difficult to recommend something without knowing budget and long term plans.