One thing both of your options so far are missing is a second HD (or SSD). It is strongly advised to capture to a different drive than the OS and software is running on.
The older HP looks capable and would have room in the case for upgrades, additional HD, etc. I have a similar age HP and the case is decent and it takes a standard power supply which is often marginal on prebuilt PCs. The CPU on that should be adequate being about equivalent to a Core 2 Duo E6700 which is a known quantity at least for ATI AIW capture system "builds" requiring an AGP slot. You don't need the AGP slot for your USB capture device so can use newer equipment. I believe the cpu on this HP could also be upgraded a bit if needed. It's hard to find the right info on this system from HP (I hate their support site!).
The Dell is definitely newer, faster, etc. but being SSF it has limitations for upgrades, esp. the PSU which is proprietary. The newer, faster part would include USB3 ports (useful) and SATA-2 drive ports, but it only has 2 of those which are both be in use if the optical drive is to be used. For me this might be a show stopper, but you can usually make do without an optical drive...
If you haven't seen it, you might want to follow along on this current thread
discussing almost the same thing.