Keep in mind that I tend to be forward looking and spend more up front to reduce costs of ownership later on. I'm also a sound production company, not a DJ company.
A chaser pack will work in one of two ways:
Either timed or triggeed. By timed, that means it will change or chase, based on an interval that may or may not be adjustable. When in trigger mode, the chaser will change based on typicaly a loud low-frequency signal, typically a kick drum makes a good trigger. Trigger systems typically use an internal microphone, bt I'm sure you could bypass that with a piezo-type drum trigger and do it your own way. However, I am not advocating modifying your gear. In either case, the channels typically go full on or full off in some combination. Programability may or may not be an option.
A dimmer pack is more complicated. A dimmer pack such as the ADJ/Elation/LSC(What is it now?) DP-DMX20L is a dimmer pack. Well, actually, it's now a hybrid dimmer pack, but I'll touch on that later. By dimming, you can adjust the intestity of the light, making dummer packs ideal for Par Can fixtures, but NOT fixtures with motors as the variable wattage output can damage motors when running less than full voltage capacity on the channel. Another neat feature about this dimmer pack is it does have built in sequences with time settings. While it does not chase to anything, you can just have it run a sequence all night. Since this is a DMX device, when you couple it with a programable DMX controller such as the DMX Operator, you can make your own sequences and chases. The DMX Operator has a built-in microphone for usage with chase sequences. Pretty cool! About that hybrid comment: I have older ones that are dimming only. The newer ones are hybrid, which means you can select any channel or channels on the unit and set them to be a switching/relay channel instead of dimming. Using the switching mode allows you to use hi-tech effects that have motors since now those channels are on/off only.
Pros of a dimmer pack: Greater flexibility down the line and can be with you long. Con: Costs a lot more, but you get a lot more. Another con: works best with a DMX controller. Pro: Works with a DMX Controller, allowing more usefulness and longer life in production.
Chaser: Pro: Less costly, can get some "activity" quickly with less over-all equipment ownership. Con: Limitations mean you'll outgrow it quickly. You'll end up not using or getting rid of this as you expand, meaning it was a waste of money. Short term: good purchase, but not a good long term investment.
You can always get more dimmer packs and slave them off your DMX controller. This solution grows with you as you grow. It requires a slightly higher knowledge base to get started, but you can figure that out in 5 minutes. Depending on the controller you get, you might need to take notes since ADJ/Elation really packs some serious punch and features into these budget-minded DMX controllers. I've had my DMX Operator 5 years now, and I'm barely using the thing. Such a shame that I've been seriously under-utilizing this bit of gear. I'm going to learn to program it and develop lots of scenes. I can use it to create complex shows and still have a compact work surface with lots of capabilities.
A DMX controller and a DP-DMX-20L is a bigger step-in than a chaser pack. Trust me, you'll thank me later on! The money IS worth it.