Its may be calculated like this,

1) Cost analysis, what you really meant by cheap dedicated servers, what is the price range i know that dedi available from $29 till $50 in the cheap range.

2) What software you want to run and the way you want to run - Dedi servers give more flexibility to planning, controlling, reinstallation, migration etc which may not be good in VPS

3) You can install and try any software in Dedi according to your need which may be a bottleneck in VPS but it depends on the company u buy VPS

In general the cost is the only factor to be considered since dedi will provide you powerful RAM and disk space which may not be there in VPS for that price range

If they have same configuration then I will recommend you to go for dedicated server instead of VPS. As vps gets shared by other users as well, so if any user on your vps node taking more resource than allocated to him then it can create some problem on the server. But this is not in the case of dedicated server, you will be the only one on a dedicated server.

Correct me if i'm wrong, but aren't there underlying resource limits placed on a VPS besides cpu/memory usage? I had a vps once and occassionally ran into memory allocation issues due to some hidden limits not discussed initially. I would personally rule for a vps for personal/business sites and a dedicated for web hosting clients. If you use cPanel, there may be some picky customers that do not like the fact that the cpanel will show that they are on a vps server. On top of this, it's hard to find good specs on a vps without some sacrifices. I do like that software licenses are cheaper for vps.

I prefer quality vps

If you need a lot of storage then dedicated might be better idea. As today you can get pretty good dual-core dedicated server with 250GB+ disk for $60-80

Lots for VPS and lots for dedicated. Given the price variance, I'd select a dedicated every day of the week. Then again, the choice boils down to your application and projection for growth. Good luck whatever you select.

I would definitely go with a cheap dedicated personally

Dedicated server is what i'd choose.

As a hosting provider I would say VPS because we make more money on the hardware. But from a hardware, consistency and resources perspective I would say go with dedicated.

Start with vps then dedicated.

A VPS is almost always better, unless you need a custom kernel.

All things equal, from the view of backup and restoring, upgrading I will go for the VPS.

I would go with dedicated. Having 100% control of the whole server is priceless to me

I would start with a VPS, and once your needs exceed those of the VPS specs, upgrade to a suitable dedicated.

The cheapest dedicated server has a lot more value than any VPS.