You could potentially try recording Rate of Perceived Exertion (RPE) and Rate of Perceived Technique (RPT). Both on a scale of 1 - 10.
RPE has been fairly well explained elsewhere, but is essentially how hard you feel you worked (so, a classic 20 rep squat session where you take your 10RM in the squat and squat it 20 times is going to be higher than polishing your guns with some cable curls).
RPT is something I've taken from the Gold Medal Bodies (GMB) training programs. The idea being that you can rate your technique on a scale of 1 to 10, based on how it feels (and possibly on video review); so if you're squatting and your knees are caving in, hips are shooting up and you're doing a bastardised good morning / squat combination, your technique rating is going to be a lot lower than if you keep your knees out, chest up and back tight the whole time.
You could also look at using some sort of heart rate monitor (yes, I know it sounds weird to use one with weight training, but I've tried it and it does reveal a surprising amount, probably because a heavy set of squats of deadlifts will make your heart try and burst out of your chest). I use one that gives you a breakdown of heart rate over the session, and an "MEP" rating for the whole workout (basically, a value of how hard you've worked. By itself, a single MEP value is relatively meaningless, but if tracked over a period of time, it gives you a measure of how hard you worked during the training session).
If you want metrics to compare, volume (so weight * (sets * reps) for total poundage moved) isn't a bad comparison to make, but that doesn't really get you the intensity.
Another option would be to get a gadget to measure bar speed, the idea being if the bar is moving slower this week for a given weight than last week, then arguably, you're training less intensely.
I would say that your best bet is a combination of techniques. In your training log (you are keeping a training log, right?), record the RPE and RPT and get a heart rate monitor as described above, then, over time, you'll be able to track how intensely your workouts are.