In my mind, three factors override everything else when selecting a self-defense handgun loading. In order of importance:
1. Reliability in my particular firearm
2. Minimum of 12" penetration in 10% Ballistic Gelatin (FBI recommendation)
3. Reliable and consistent expansion
In major caliber handguns (.38+P/9mm and up) I expect all three of those criteria to be met and in minor calibers (standard pressure .38 Special/.380 Auto and smaller) I will sacrifice number 3 if necessary to get numbers 1 and 2.
As to whether or not "budget line" JHP's can meet these criteria, it depends on the particular caliber and loading as some can while others can't. Because the OP specifically mentioned 9mm and .45 ACP, I'll address those cartridges specifically. While I use premium ammo in my .45 (Federal HST), I would feel comfortable using a "budget line" JHP like WWB, UMC, or American Eagle if cost or availability was an issue with the premium fodder. Even with older bullets, a .45 is able to have a large enough HP cavity to expand reliably even at low velocity and enough weight to penetrate adequately.
With a 9mm, however, I will only use premium loadings (my current choice is Winchester Ranger). The problem with older 9mm JHP loadings is that you often have to sacrifice either expansion or penetration. With dated bullets, you usually have to use a 115gr or lighter bullet in order to get enough velocity for reliable expansion with a 9mm. Unfortunately, this combination with dated bullets often yields lackluster penetration in the 8-10" range. The other side of the coin is a heavier 147gr bullet at lower velocity. While this does penetrate well, the 9mm cartridge simply cannot drive older bullets of that weight fast enough to expand reliably. Newer bullet designs allow light, fast 9mm loadings to have controlled expansion and thus penetrate adequately and heavier, slower 9mm loadings to expand more reliably at lower velocities.
Also, premium JHP loadings really aren't that much more expensive than "budget line" JHP's if you know where to look. Midway currently lists WWB 9mm 115 or 147gr JHP for $18.79 for a 50 round box and WWB .45 ACP 230gr JHP for $32.49 for a 50 round box. That does indeed seem much cheaper than premium JHP's if you only look at the commercially packaged stuff usually encountered at big box stores, but premium JHP can be had in LEO packaging for greatly reduced prices from sources like SG Ammo and Ammunition To Go. SG Ammo currently has Winchester Ranger 9mm in standard pressure, +P, and +P+ loaded with SXT/T-Series or bonded bullets for $19.95-$28.95 for a box of 50 depending on the particular loading. Likewise, the have Winchester Ranger .45 ACP in both standard pressure and +P loaded with either T-Series or bonded bullets for $29.95-31.95 for a box of 50 depending on the particular loading.