I´ve never used an HD PVR, but I have used an Elgato. In my opinion, Elgato is pretty bad, mostly because of the software that you use with it. It's constantly freezing, lagging, and messing up my recordings.
That sounds more like your PC is struggling to handle the encoding side. If your CPU is struggling try changing the video codec options & tweaking it, changing the slider from Best quality to best performance, and choosing whether to use software or GPU as the decoder & encoder. (See image below/attached). Otherwise, OBS/OBS Studio is compatible with the Elgato capture cards, you could try using that as an alternative but I think the issue might be the same, it will process differently to using recording software directly on a PC.
Ironically I'm gonna say both are kind of s**t but for 2 different reasons. Last time I used a HD PvR it was nothing but a hassle to set it up and in the end, I found out it was incapable of recording 5.1 audio despite listing it as an ability and supporting optical (although this is a blessing in disguise lol), performance wise it wasn't that great either, limited with settings like bit/data rates being limited to max 10mbps at the time & frame rates were stuck at 30 (this was a good few years ago though, software
might have been updated by now). There's also the limitations with new gen consoles you need to take into account, so either way, the HD PvR is technically outdated.
Elgato is the least s**t of any capture device in the market, in fact it's actually the best. I dislike them solely because of their customer service and the amount of times they've mislead & ****** me around, which has cost me money, twice. The device & software are really damn good though.
It's got good customisation, lets you save & split; audio commentary, gameplay footage & webcam overlays into their own files. You can change which encoder to use & bit rates can go as high as 40mbps, unneeded but the option is there at least. You can have stream overlays and a whole heap of other b******t for that. I only use the video recording side of it though.
I would highly advise being careful with the inbuilt commentary recording, I've been burned by it a few times that I just can't trust it enough, so I stick with Audacity while using Elgato for video. Elgato also have a comparison sheet on their website showing you the differences between all their device variations, i.e. HD, HD60, HD60 Pro etc...