Both opto-chemical process and milling can produce good results, and both require skill, practice, specialized workplace and some investment in tools & materials.
IMHO, however, milling is often way overrated (treated as a simple, turn-key solution, what it isn't) while the chemical process is way underrated. For some odd reason, it seems that it's hard to discuss in civil (non-aggressive) ways; I guess people might have issues with the concept of needing "chemicals", and they like the concept of fully automated, one-step manufacturing so much that they tend to sometimes get religious about it. (edit: this is not in response to anyone in this thread.)
I've done a lot of PCBs by etching, and at 8/8 mils tracks/clearance, the copper quality is almost on par with commercial manufacturers, it's just lacking plated-through holes, high-quality soldermask and of course, multilayer.
On a limited budget, chemical process will get you way better copper resolution per money. A good etch tank and UV exposure unit are at least an order of magnitude easier and cheaper to build than a good CNC mill.
OTOH, for drilling the holes, you most likely still need some kind of CNC machine anyway, although a lot simpler machine with mechanical play that would never produce acceptable milling results, will suffice for drilling holes at exact locations, especially as you can compensate for mechanical play in software by approaching each hole from the same direction. Many of the "cheapo" DIY CNC kits are almost able to do high-quality CNC milling, but not quite; whereas they are more than enough for CNC hole drilling. For hole drilling, the base doesn't need to be leveled and the workpiece mounting is trivial as there are no sideway forces.
Since the chemical process requires so many seemingly tedious steps that each take some practice to perform correctly, not to mention the need for separate CNC drilling step, I understand very well why PCB CNC milling looks so appealing. But as usual in engineering, it's completely different to imagine a technical need or concept, and to provide a really working implementation that matches the expectations. PCB milling is often unsatisfactory on hobbyist budgets. For professional sector, some machines perform better, others require a separate operator to be hired in practice due to maintenance-requiring or hard-to-use design; I've heard from several professional sources that the LPKF machines have been especially painful and disappointing in this regard as they didn't provide the turn-key simplicity they were bought for, although, this might have changed with the company feedback and design of new models.