Comparing both options on the following criteria may assist.
Portability: Most dedicated DSP pedals, boxes, etc are more portable than hauling a desktop and running DSP software on it. However a laptop, tablet, or iPad, or even the possible use of a smart phone with appropriate apps may now be a serious contender in the portability arena.
Latency: This is not an issue with dedicated boxes vs software. Latency is an issue with some software DSP products but not all and this largely depends on the hardware platform age and performance. Generally the better the DSP software product and the newer the platform this should not be an issue.
Cost: older dedicated DSP devices will likely be cheaper than buying a laptop and pro DSP software.
Maintenance: as a rule of thumb the older the technology the more costly to repair or replace. New gear will likely have at least a 90 day warranty while desktops and laptops will likely have at least a 1 year warranty with the option to extend it to 5 years.
Robustness: How fragile is that foot pedal vs your laptop? not much, where laptops often break as soon as they hit the floor.
Versatility: Software generally wins on this one as there is usually a ton of plug ins available with each new revision level especially with Pro versions where as dedicated boxes are at best one trick ponies.
Difficulty in setting up: I don't know about you but when I jam I want to spend most of my time making music and not futzing around with my gear. Whether a dedicated DSP box vs DSP software requires more attention in configuring is going to be very specific to the gear you choose. Either one could be a nightmare or a walk in the park.
If you can compare one set up vs the other than that is the best way for you to find out which one is worth the investment as you have first hand experience.
I suggest you look at what is available here for Jamming:
Their solution is cost effective, portable, with zero latency, and easy to setup. Imagine, you can have 7 performers in your living room having a jam session with ear phones plugged in, no worries about neighbors calling the cops--your parents will love you.