I've been participating in HP Cloud's closed beta program, and they have now announced their billing They use the same cloud system and API as Rackspace, making it a fair comparison. (See Rackspace cloud server pricing and Rackspace cloud file pricing)
Executive summary: HP have priced themselves slightly lower, but don't have the two smallest server configurations. So, Rackspace is still better than HP or Amazon EC2 if you just need something minimal, as I described here.
(2012-08-15 UPDATE: Rackspace are stopping their minimal server config: no more 256MB option in their "nextgen" V2 API. Also scheduled images are not available in the V2 API (yet).)
HP offer slightly less disk space than Rackspace, for the same memory size. HP's bandwidth is slightly cheaper than Rackspace; incoming bandwidth is free on both.
HP's CDN offering is weird; based on your billing location, rather than where your servers are, or where your customers are! If you are a U.S. or European company it is cheaper. If not it is more expensive. However, for Japan, HK, Singapore it is only a fraction more expensive, so not a showstopper. Also it is tiered: if you're spending more than $200/month on CDN bandwidth it will work out cheaper still.
If your headquarters are not in North America, Europe, Latin America,
Japan, Hong Kong or Singapore then HP pricing says they'd rather you took your CDN business elsewhere.
( 2012-06-12 UPDATE: I've added a surprise Linux cloud hosting option to the below: Microsoft Azure! They are competitive at the low end: 1GHz CPU, 768MB RAM, 25GB storage, 4GB outbound bandwidth (inbound is free), is $12.51/month (about 1.5c/hr). An extra 20% discount for paying for 6 months. But also reasonable at the high-end too (except 14GB is the most memory they can offer). (price calculator) )
Comparing HP's cheapest option to the closest (based on memory size) alternative:
HP: 1Gb RAM, 30GB disk, 1 virtual core: $0.04/hr ($29/month)
Rackspace: 1Gb RAM, 40GB disk, 1/16th of a 4-CPU server: $0.06/hr ($43.80/month)
EC2 Small: 1.7GB RAM, 160GB disk, 1 virtual core, $0.08/hr ($58/month)
Azure Small: 25GB disk, $0.08/hr ($60/month)
(NB. the XSmall, with 768MB RAM, 1Ghz CPU is $12.50/month)
At the top of the CPU range:
HP: 32GB RAM, 960GB disk, 8 virtual cores: $1.28/hr ($934/month)
Rackspace: 31GB RAM, 1200GB disk, 4-CPUs: $1.80/hr ($1,314/month)
EC2, High-CPU Extra Large:7GB RAM, 1690GB disk, 8 virtual cores (20 compute units): $0.66/hr ($481/month)
EC2, High-Memory Quadruple Extra Large: 68GB RAM, 1690GB disk, 8 virtual cores (26 compute units): $1.80/hr ($1,314/month)
, 975GB disk: $0.64/hr ($575/month)
(So, if you are CPU bound then Amazon is best, if memory bound then HP is best.)
Overall, the pricing seems reasonable. However Rackspace have a brand oozing stability and reliability, and Amazon are huge and have data centres all over the world, so I'm not sure HP prices are low enough to worry their competitors. The 50% discount during the beta program makes them a good buy, short-term, though!