Slicehost is an excellent hosting platform - I've been using them for some time now. However, in the interest of trying to drive costs down to absolute zero, I started evaluating Heroku as a platform to host this site.
Slicehost
If you're not familiar, Heroku and Slicehost differ structurally: Slicehost provides you with a virtual instance of Linux - most major distributions are available. It's your job to configure/manage the web application framework.
This opens a world of flexibilty - you can deploy any web-based solution you like backed by the database of your choosing. This is incredibly empowering - but you own everything, including downtime (at least downtime not incurred by Slicehost), maintenance updates, security, etc.
Speaking of downtime incurred by Slicehost, I want to call out that I have a slice that has been running 24-7 for 11 months. Sanity dictates that you'd want to have regular scheduled backups of your VM (they do this for an additional recurring fee), but I feel pretty good that I haven't had to reprovision my server.
Heroku
Heroku, is quite different. They don't provide a virtual machine in the "cloud" (I really hate buzz words sometimes) - rather, they provide a full server solution with the Ruby on Rails framework sitting firmly on top of it. The pitch goes something like this (heavily paraphrased) - Heroku handles all server administration so you can focus on the business solution - i.e. webapp code.
That's actually pretty cool because you can build your web site and then deploy without having to provision servers, performance tune databases, or deal with runaway processes. However, you get all this at the cost of options.
Heroku is specifically a Ruby on Rails platform - if you want to build your app in Python, Java, or .Net, you'll want to look elsewhere. If you are planning to build your app in ruby, you'll have to accept some restrictions. Additional services such as full text indexing use WebSolr, sending mail messages requires their Sendgrid service. This isn't necessarily bad, but it does reduce the vast myriad of options normally available to Rails applications.
Flat fee vs. a la carte
You can start using Slicehost for $20 a month - not bad at all for a new web app that is not yet commanding a lot of bandwidth. Like most other VPS hosting services, you can scale up your VM by paying more.
Heroku charges by the feature. You can start a small site at no charge. If you can limit the add-ons they provide and your DB storage needs are small, you can get away with running your site for free... that is until you start experiencing serious traffic. However, if you need greater concurrency or more database storage, you'll have to start paying monthly fees. Include a few of their intermediate or pro add-ons, and the price goes up quickly.
Some Quick Stats
I ran the apache benchmark tool against two instances of the same web app - one on Slicehost the other on Heroku, to get a feel for how their basic plans compared. I used the following two commands:
ab -c 10 -k -n 1000 http://choltz.com/
If you're not familar with it, ab is the apache bench utility - it's great for simple concurrency tests. chrisholtz.com is hosted on Heroku and choltz.com on Slicehost. Here are some highlights:
Requests per second: 59.96 [#/sec] (mean)
Heroku
Requests per second: 49.79 [#/sec] (mean)
Time per request: 20.085 [ms] (mean, across all concurrent requests)
The Slicehost instance was running an apache web server with a reverse proxy, pointing at Phusion Passenger with two ruby instances. The Heroku instance was running a base deployment with one dyno.
Slicehost yields slightly better performance in this test and I suspect that this could be improved slightly by using using Ruby 1.9 (this test used Ruby 1.8.7). Still, the difference in performance is pretty slim. I don't think 3.5 ms tilts the scales much in this case.
The full benchmark results can be found here (Slicehost) and here (Heroku).
The Bottom Line
If you're looking for a low bandwidth web app or small-scale invite-based test program, both web hosts provide a decent platform. Which you choose will largely be dictated by the gems (addons) your app needs and how much control you want over your server environment.